Comments on avalanche flow models based on the concept of random kinetic energy

TL;DR

This paper critically reviews avalanche flow models based on random kinetic energy, highlighting inconsistencies with established granular flow physics and suggesting improvements for more accurate modeling of snow avalanches.

Contribution

It provides a detailed critique of existing RKE-based avalanche models, identifying key assumptions that conflict with granular flow theory and proposing directions for model refinement.

Findings

Original RKE model assumptions differ from dense granular flow physics.

Variable-density model's energy balance leads to a third-order equation, contrary to expectations.

Suspension layer model neglects gravity and established particulate flow results.

Abstract

In a series of papers, Bartelt and co-workers developed novel snow-avalanche models in which \emph{random kinetic energy} $R_K$ (a.k.a.\ granular temperature) is a key concept. The earliest models were for a single, constant density layer, using a Voellmy model but with $R_K$-dependent friction parameters. This was then extended to variable density, and finally a suspension layer (powder-snow cloud) was added. The physical basis and mathematical formulation of these models is critically reviewed here, with the following main findings: (i) Key assumptions in the original RKE model differ substantially from established results on dense granular flows; in particular, the effective friction coefficient decreases to zero with velocity in the RKE model. (ii) In the variable-density model, non-canonical interpretation of the energy balance leads to a third-order evolution equation for the flow depth or density, whereas the stated assumptions imply a first-order equation. (iii) The model for the suspension layer neglects gravity and disregards well established theoretical and experimental results on particulate gravity currents. Some options for improving these aspects are discussed.